Sensitivity and Mathematical Analysis of Malaria and Cholera Co-Infection
G. A. Adeniran *
Department of Physical Sciences, Chrisland University, P.M.B. 2131, Abeokuta, Ogun State, Nigeria.
I. A. Olopade
Department of Mathematics and Statistics, Federal University, Wukari, P.M.B. 1020, Taraba State, Nigeria.
S. O. Ajao
Department of Computer and Mathematics, Elizade University, P.M.B. 002, Ilara-Mokin, Ondo State, Nigeria.
V. A. Akinrinmade
Department of Mathematics/Statistics, Osun State College of Technology, Esa-Oke, Osun State, Nigeria.
O. R. Aderele
Department of Mathematics and Statistics, LASUSTECH, Ikorodu, Lagos State, Nigeria.
S. O. Adewale
Department of Pure and Applied Mathematics, LAUTECH, P.M.B. 2000, Ogbomoso, Oyo State, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
In order to better understand the factors affecting the dynamical spread of cholera and malaria in a community, we defined a new fourteen (14) compartmental mathematical model in this study. The model is examined for each of the factors influencing the spread of the disease in an effort to identify those that are most sensitive. First, full models of malaria-cholera co-infection were studied, then sub models of malaria and cholera alone. For the purpose of determining whether disease-free and endemic equilibrium points exist, the stability of the malaria model alone, the cholera model alone, and the entire model of malaria-cholera co-infection were all examined. The disease-free equilibrium point has been demonstrated to be locally asymptotically stable whenever the threshold is below unity and unstable whenever the threshold exceeds unity using the Next Generation Matrix Method (NGM). Calculations are made to determine the model's relative sensitivity solution for each parameter. To demonstrate the impact of each parameter on the dynamical spread of malaria-cholera co-infection, numerical solutions utilizing the differential transformation approach were performed by Maple software. Sensitivity analyses showed that the transmission rate was the most sensitive of all the model's parameters. Sensitivity analyses revealed that out of all the parameters involved in the model, the transmission rate (\(\beta\) M), low immunity rate (\(\varepsilon\)1 ) and mosquito biting rate (\(\alpha\)) for Malaria model, transmission rate (\(\beta\) c) and low immunity rate (\(\varepsilon\)2 ) for Cholera model, transmission rate (\(\beta\) Mc) and low immunity rate (\(\varepsilon\)3) for the co-infection model were of high influence on their basic reproduction numbers. While (\(\tau\)4) is the rate of treatment for co-infection with malaria and cholera, which has a negative impact and lowers the basic reproduction rate. The consequence is that it will be challenging to eradicate or stop the spread of the two illnesses in the population if the reproduction rate for malaria/cholera co-infection keeps rising. The rate of treatment (\(\tau\)4) reduction in fundamental reproduction of Malaria/Cholera Co-infection, which makes it convenient to stop the spread of the two infections. Therefore, efforts must be made to decrease the rate at which each person comes into contact with the two diseases, and ongoing care for those who are infected in the community is necessary to maintain a disease-free environment.
Keywords: Malaria, cholera, reproduction number, critical points, sensitivity analysis, stability